Question: Simplify. Rewrite the expression in the form $9^n$. $9\cdot 9^2=$
$\begin{aligned} 9\cdot 9^2&=9^1\cdot 9^2 \\\\ &=9^{1+2} \\\\ &=9^{3} \end{aligned}$ This follows from the general rule $x^m\cdot x^n=x^{m+n}$. Note that the powers have the same base. We can also see this is correct by expanding the powers. $\begin{aligned} 9\cdot 9^2&=\underbrace{9}_\text{1 time}\cdot\underbrace{9\cdot 9}_\text{2 times} \\\\\\ &=\underbrace{9\cdot 9\cdot 9}_\text{3 times} \\\\ &=9^{3} \end{aligned}$ In conclusion, $9\cdot 9^2=9^{3}$.